MATH101 Lecture Notes - Trigonometric Substitution, Partial Fraction Decomposition, Power Rule
Document Summary
Limits: the limit of a function is the value that the function approaches as the input approaches a certain value. It is de ned as the limit of the difference quotient as the change in the input approaches zero. For example, the power rule states that the derivative of f(x) = x^n is f"(x) = nx^(n-1). The product rule states that the derivative of f(x)g(x) is f"(x)g(x) + f(x)g"(x). For example, if a ball is thrown upward with an initial velocity of 20 m/s, its height h (in meters) at time t (in seconds) is given by h(t) = -5t^2 + 20t. The maximum height occurs when t = 2 seconds, and the maximum height is 20 meters. Integrals: integrals are the reverse of derivatives, they represent the area under a curve. The de nite integral of f(x) from a to b is the area under the curve of f(x) between x = a and x = b.
